Consider the function X(x, y) 1 x²+y²+1° Please find equations for the following level surfaces for A, and sketch them: i. X(x, y) = ii. X(x, y) = 1o Please find k such that the level surface X(x, y) = k consists of a single point.

Q: Let f (z, y) = 4x+y. Find the slope of the surface z = point (1, -1). f (T, y) in the y-direction at…

A:

Q: 3. cos Tx – x*y + e*z + yz = 4 at point Po(0, 1, 2). -

A: The given surface at the point P0 is    Cos(pix) - x2y +exz + yz = 4

Q: find an equation for the plane that is tangent tothe given surface at the given point.11. z = ln (x2…

A: To find an equation for the plane that is tangent to the given surface at the given point. Given…

Q: The equation of tangent plane to the surface f(x,y, z) x+ y +z-9 0 at the point (1,2,4) is x+y+z=…

A:

Q: Find an equation of the tangent plane to the surface g(x, y) = x2 + y2, at the given point (1, −1,…

A: We have given the surface; g(x, y) = x2 + y2 and the point (1, −1, 2)

Q: The tangent plane to the surface with equation at the point where (x, y) = (1,0) has the equation z…

A: According to guidelines I solve the first question only.So kindly request you to repost the…

Q: find an equation for the plane that is tangent tothe given surface at the given point. z = ln (x2 +…

A: The given function is It can be written as as the given function has both variables x and y.

Q: Given z = f(x, y) = Vx2 + y² + 4y. (a) Find its domain and range. (b) Sketch the level curves for z…

A:

Q: I. Find an equation of the tangent plane to the surface at the given point. a. f(x,y) = x² – 2xy +…

A: Given point is (1, 2, 1).

Q: Find an equation of the tangent plane to the surface z = x2 + y2 + 2 at the given point (1, 3, 12)

A: Given surface, So

Q: Given a surface f(x,y) = 0x + (4)y. Find the derivative in the direction of v = at the point (6,…

A:

Q: 2. For the surface z = In(y+ Vx² + y²). (a) Find an equation of the tangent plane at the point (3,…

A:

Q: Find the slopes of the surface in the x- and y-directions at the given point. h(x, y) = x2 − y2 (-2,…

A:

Q: Find the equation of the tangent plane to the surface z = e17 In(1y) at the point (-3, 1,0). Note:…

A:

Q: At which of the points below is the tangent plane to the surface x² – 2y + z + yz = 2 vertical?…

A:

Q: Find an equation for the plane that is tangent to the given surface at the given point. z= vy-x…

A: Here, the given surface is: z=y-x Now, ∂z∂x=12y-x(-1)=-12y-x∂z∂y=12y-x(1)=12y-x Now, at (0,4,2):…

Q: Find the equation of the tangent plane to the surface z = 9y? – 4x² at the point (-3, –3, 45). e:…

A: Given query is to find equation of the tangent plane.

Q: Find the equation of the tangent plane to x² the surface z = + y? 4 - at the point (2, 3, 10) x + 6y…

A: The equation of the tangent plane to a surface f(x,y,z) is given by:

Q: Find an equation for the plane tangent to the surface e z = x cos(xz) – y at the point (2, 1,0).

A:

Q: 16)Consider the equation of the surface S given by In (xyz) + xyz + x3 - y3 + z3 = 2 An equation for…

A:

Q: for y^2 - z^2 =1, find the point(s) on surface nearest to origin

A:

Q: Find the equation of the tangent plane to x2 the surface z = 4 + y? at the point (2, –2, 5)

A:

Q: The level surface of f(x, y, z)=Vx²+y² -5_of height 2 is O a. A circle of radius /2 O b. A cylinder…

A:

Q: Find an equation of the tangent planes to the given surface at the specified point. (a) f(x,y)= 4x…

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question.

Q: For the level curve f(x,y,z)=12 for f(x,y,z)= 4x2 − 2y2 + z2 at the point (2,2,2), find the…

A:

Q: Given a surface f(x,y) = -2x² + (-3)y“. Find the derivative in the direction of v = at the point…

A:

Q: 11. What is the equation of the surface revolved about the x-axis for 2² - xz = ln x + 3x? A. y²…

A: Introduction: When a surface is revolved around the coordinate axis, another surface is obtained. In…

Q: A surface is represented by the following multivariable function, f(x,y) = x+y³ - 3x- 3y+1 a)…

A: Consider the given function fx,y=x3+y3-3x-3y+1. Obtain fx and fy as follows.…

Q: sketch a typical level surface for the function. ƒ(x, y, z) = ln (x2 + y2 + z2)

A: The given function is  ƒ(x, y, z) = ln (x2 + y2 + z2). In order to sketch the typical level surface…

Q: Given a surface f(x,y) = -3x² + (-4)y“. Find the derivative in the direction of v = at the point…

A:

Q: Given a surface f(x,y) = -2x² + (5)y². Find the derivative in the direction of v = at the point (7,…

A:

Q: The equation of the tangent plane to the surface X +y- z = (2, –1, -1) is 2 at the point | O a) None…

A: This question can be solved by applying the formula of equation of tangent plane to the given…

Q: et T(x, y, z)= 100+ x² + y² represent the temperature at each point on the sphere x² + y² + z² = 80.…

A: Given: Tx,y,z=100+x2+y2sphere g= x2+y2+z2=80plane h =x-z=0

Q: Find an equation of the tangent plane to the surface at the given point in the figure below.

A: Consider the given:…

Q: Find the positively oriented simple closed curve C for which the value of the line integral     (y3…

A: The line integral is  ∫C(y3 − y) dx − 9x3dy The expression for Green's theorem is  ∫CP(x,y) dx…

Q: The roof of the Monterrey Campus gymnasium has the shape of the hyperbolic paraboloid given by the…

A: Here we have to use directional derivative  Directional derivative of a function f(x,y,z) in the…

Q: Find an equation of the tangent plane to the given surface at the specified point. z = 4(x - 1)2 +…

A: We have equation of the form     z= f(x, y)  And we have to find equation of tangent plane to the…

Q: 1. Let z = f(x, y) be the function of two variables given by z = 8 – x2 – y? + 2y. (i) Find the…

A: A function f(x) is a rule that is used to fix or associate a number to the particular point on the x…

Q: 3. (a) Show that the two surfaces S₁ z = xy and S₂ : 2 = x² - y² intersect perpendicularly at the…

A: Introduction: The gradient of a surface is a vector quantity that is directed in the normal…

Q: Given w = f (x, y, z) = 4.x² + y² + 4z². Sketch the level surface of the function for w = 1.

A: We have to sketch the level surface of the following function for w=1, w=f(x,y,z)=4x2+y2+4z2

Q: Find an equation of the plane tangent to the following surface at the given points. z =6 cos (x- y)+…

A:

Q: Find an equation of the plane tangent to the following surface at the given points. 元 z= 4 cos (x-…

A:

Q: Consider the paraboloid f(x.y) = 23- 25 and the point P (5V5,6) on the level curve f(x.y) = 14.…

A:

Q: Given a surface f(x,y) = -3x² + (3)y². Find the derivative in the direction of v = at the point (5,…

A:

Q: b. Find an Equation for the tangent plane and normal line at the points Po on the given surface. x +…

A: Tangent palane and line equation

Q: Find the equation w=T(x,y,z) of the tangent hyperplane at p. F(x,y,z)=3x²-2y²+xz², p=(1,2,-1)

A: General equation for the tangent to the plane is expressed as:…

Q: Find the surface area of the rotating object from the curve y = x^2 with the constraint 0 ≤ x ≤ 1…

A: The formula for the surface area of the rotating object from the curve y=f(x) with the constraint…

Q: Find the equation of the tangent plane to the surface z = x² +y² + 1 at the point (1,1,3). Write the…

A: use the equation of tangent  plane for the given surface.

Q: Below is a curve C, which is the intersection between the surfaces  S1 : z = 4 − x2 S2 : z + 2x −…

A: Given that,Below is a curve C, which is the intersection between the surfaces   S1 : z=4−x2  S2 :…

Q: Given w = f(x, y, z) = 4r + y + 4z². Sketch the level surface of the function for w = 1.

A: For the function of the form: w=fx, y, z, the level surfaces are defined using the equation, f(x, y,…